# MTH603 Quiz 2 Solution and Discussion

• Which of the following reason(s) lead towards the numerical integration methods?

• In Trapezoidal rule, we assume that f(x) is continuous on [a, b] and we divide [a, b] into n subintervals of equal length using the ………points.

• Given that dydt=t+y√ with the initial condition y0=1att0=0 find the 3rd term in Taylor series when t=1, y/ =0.2, y// =2, and h=0.1.

• Given that dydt=y−ty+t with the initial condition y=1,t=0 Using Euler’s method, y at
h=0.01
; the value of y(0.01)is

• Given that dydt=1−y√ with the initial condition y0=1att0=0 find the 3rd term of Taylor series when t=0.5 and y// =0.25.

• While employing Trapezoidal and Simpson Rules to evaluate the double integral numerically, by using Trapezoidal and Simpson rule with respect to -------- variable/variables at time

Single
Both

• At which of the following points the Maximum value of 2nd derivative of function
f(x) = -(2/x) in the interval:[1,4] exits?

At x=1

• At which of the following points the Maximum value of 2nd derivative of function
f(x) = -(2/x) in the interval:[1,4] exits?

• Given that dydt=t+y√ with the initial condition y0=1att0=0 find the 2nd term in Taylor series when t=1, y/ =0.2, and h=0.1.

• In Trapezoidal rule, we assume that f(x) is continuous on [a, b] and we divide [a, b] into n subintervals of equal length using the ………points.

n
n+1
n-1
None of the given choices

• In Simpson’s rule, we can estimate the integral by …………the areas under the parabolic arcs through three successive points.
Subtracting
Multiplying
None of the given choices

• Trapezoidal rule of integration of a definite integral is of…………

O(h2)
O(h3)
O(h4)
None of the given choices

• Which of the following method is simplest one to integrate numerically a given tabular function but give more error?

Rectangular method
Trapezoidal method
Simpson’s 1/3 Rule
Simpson’s 3/8 Rule

Trapezoidal method

• Which of the following method is simplest one to integrate numerically a given tabular function but give more error?

Rectangular method
Trapezoidal method
Simpson’s 1/3 Rule
Simpson’s 3/8 Rule

• Given that dy/dt=t+y with the initial condition y0=1at t0=0 find the 3rd term in Taylor series when t=1.5 and y// =0.6

65

43

33

1

3

2

1

3
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